Even though it is usually assumed that data centers can always operate at maximum capacity, there have been recent scenarios where the amount of electricity that can be used by data centers evolve over time. Hence, the number of available processors is not a constant anymore. In this work, we assume that jobs can be checkpointed before a resource change. Indeed, in the scenarios that we consider, the resource provider warns the user before a change in the number of processors. It is thus possible to anticipate and take checkpoints before the change happens, such that no work is ever lost. The goal is then to maximize the goodput and/or the minimum yield of jobs within the next section (time between two changes in the number of processors). We model the problem and design greedy solutions and sophisticated dynamic programming algorithms with some optimality results for jobs of infinite duration, and adapt the algorithms to finite jobs. A comprehensive set of simulations, building on real-life job sets, demonstrates the performance of the proposed algorithms. Most algorithms achieve a useful platform utilization (goodput) of over 95%. With infinite jobs, the algorithms also keep fairness by having a relative minimum yield above 0.8, meaning that each job gets a good access to the platform (80% of the time that it would have had if each job had its perfect share of the platform). For finite jobs, the minimum yield can be low since very short new jobs may have to wait until the beginning of the next section to start (and finish), significantly impacting their yield. However, for 75% of the jobs within each workload, the yield ratio between these jobs is at most at a factor two, hence demonstrating the fairness of the proposed algorithms.

High-performance computing centers and cloud providers host a wide variety of workloads, ranging from routine calibration tasks with no strict timing requirements to urgent real-time computations that must be completed within hard deadlines. Traditional approaches reserve resources for high-criticality tasks or preempt and kill lower-criticality tasks when necessary, resulting in wasted compute time and longer turnaround times for lower-criticality tasks. We suggest that a better solution is to interleave the execution of critical and non-critical tasks. We formulate a bi-objective optimization problem: guarantee that all critical tasks meet their deadlines, and minimize the maximum flow, defined as the time a task spends in the system, of non-critical tasks. We introduce a formal model, derive an approximation algorithm and a lower bound, and develop several heuristics based on the approximation framework. Through extensive simulations, based on synthetic and real-world workloads, we show that one of our heuristics reduces the maximum flow of non-critical tasks by up to 14% compared to static resource partitioning.

Lossy compression and asynchronous I/O are two of the most effective solutions for reducing storage overhead and enhancing I/O performance in large-scale high-performance computing (HPC) applications. However, current approaches have limitations that prevent them from fully leveraging lossy compression, and they may also result in task collisions, which restrict the overall performance of HPC applications. To address these issues, we propose an optimization approach for the task scheduling problem that encompasses computation, compression, and I/O. Our algorithm adaptively selects the optimal compression and I/O queue to minimize the performance degradation of the computation. We also introduce an intra-node I/O workload balancing mechanism that evenly distributes the workload across different processes. Additionally, we design a framework that incorporates fine-grained compression, a compressed data buffer, and a shared Huffman tree to fully benefit from our proposed task scheduling. Experimental results with up to 16 nodes and 64 GPUs from ORNL Summit, as well as real-world HPC applications, demonstrate that our solution reduces I/O overhead by up to 3.8× and 2.6× compared to non-compression and asynchronous I/O solutions, respectively.

This paper introduces and assesses novel strategies to schedule firm semi-periodic real-time tasks. Jobs are released periodically and have the same relative deadline. Job execution times obey an arbitrary probability distribution and can take either bounded or unbounded values. We investigate several optimization criteria, the most prominent being theDeadline Miss Ratio(DMR). All previous work uses some admission policies but never interrupt the execution of an admitted job before its deadline. On the contrary, we introduce three new control parameters to dynamically decide whether to interrupt a job at any given time. We derive a Markov model and use its stationary distribution to determine the best value of each control parameter. Finally we conduct an extensive simulation campaign with 16 different probability distributions. The results nicely demonstrate how the new strategies help improve system performance compared with traditional approaches. In particular, we show that (i) compared to pre-execution admission rules, the control parameters make significantly better decisions; (ii) specifically, the key control parameter is to upper bound the waiting time of each job; (iii) the best scheduling strategy decreases theDMRby up to 0.35 over traditional competitors.

This paper discusses evaluation criteria and scheduling strategies for the analysis of overloaded real-time systems. This work builds upon techniques from queueing theory and proposes a new approach for real-time systems.

Low energy consumption and high reliability are widely identified as increasingly relevant issues in real-time systems on heterogeneous platforms. In this paper, we propose a multi-criteria optimization strategy to minimize the expected energy consumption while enforcing the reliability threshold and meeting all task deadlines. The tasks are replicated to ensure a prescribed reliability threshold. The platforms are composed of processors with different (and possibly unrelated) characteristics, including speed profile, energy cost and failure rate. We provide several mapping and scheduling heuristics towards this challenging optimization problem. Specifically, a novel approach is designed to control (i) how many replicas to use for each task, (ii) on which processor to map each replica and (iii) when to schedule each replica on its assigned processor. Different mappings achieve different levels of reliability and consume different amounts of energy. Scheduling matters because once a task replica is successful, the other replicas of that task are cancelled, which calls for minimizing the amount of temporal overlap between any replica pair. The experiments are conducted for a comprehensive set of execution scenarios, with a wide range of processor speed profiles and failure rates. The comparison results reveal that our strategies perform better than the random baseline, with a gain of 40% in energy consumption, for nearly all cases. The absolute performance of the heuristics is assessed by a comparison with a lower bound; the best heuristics achieve an excellent performance, with an average value only 4% higher than the lower bound.

Modern computing platforms commonly include accelerators. We target the problem of scheduling applications modeled as task graphs on hybrid platforms made of two types of resources, such as CPUs and GPUs. We consider that task graphs are uncovered dynamically, and that the scheduler has information only on the available tasks, i.e., tasks whose predecessors have all been completed. Each task can be processed by either a CPU or a GPU, and the corresponding processing times are known. Our study extends a previous 4√m/k-competitive online algorithm by Amaris et al. [1], where mis the number of CPUs and k the number of GPUs (m≥k). We prove that no online algorithm can have a competitive ratio smaller than √m/k . We also study how adding flexibility on task processing, such as task migration or spoliation, or increasing the knowledge of the scheduler by providing it with information on the task graph, influences the lower bound. We provide a (2√m/k+1)-competitive algorithm as well as a tunable combination of a system-oriented heuristic and a competitive algorithm; this combination performs well in practice and has a competitive ratio in Θ(√m/k). We also adapt all our results to the case of multiple types of processors. Finally, simulations on different sets of task graphs illustrate how the instance properties impact the performance of the studied algorithms and show that our proposed tunable algorithm performs the best among the online algorithms in almost all cases and has even performance close to an offline algorithm.

This work introduces scheduling strategies to maximize the expected number of independent tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The cloud platform is composed of several types of virtual machines (VMs), where each type has a unit execution cost that depends upon its characteristics. The amount of budget spent during the execution of a task on a given VM is the product of its execution length by the unit execution cost of that VM. The execution lengths of tasks follow a variety of standard probability distributions (exponential, uniform, half-normal, etc.), which is known beforehand and whose mean and standard deviation both depend upon the VM type. Finally, there is a global available budget and a deadline constraint, and the goal is to successfully execute as many tasks as possible before the deadline is reached or the budget is exhausted (whichever comes first). On each VM, the scheduler can decide at any instant to interrupt the execution of a (long) running task and to launch a new one, but the budget already spent for the interrupted task is lost. The main questions are which VMs to enroll, and whether and when to interrupt tasks that have been executing for some time. We assess the complexity of the problem by showing its NP-completeness and providing a 2-approximation for the asymptotic case where budget and deadline both tend to infinity. Then we introduce several heuristics and compare their performance by running an extensive set of simulations.

This paper revisits the real-time scheduling problem recently introduced by Haque, Aydin and Zhu (2017). In this challenging problem, task redundancy ensures a given level of reliability while incurring a significant energy cost. By carefully setting processing frequencies, allocating tasks to processors and ordering task executions, we improve on the previous state-of-the-art approach with an average gain in energy of 20%. Furthermore, we establish the first complexity results for specific instances of the problem.

This work deals with scheduling and checkpointing strategies to execute scientific workflows on failure-prone large-scale platforms. To the best of our knowledge, this work is the first to target fail-stop errors for arbitrary workflows. Most previous work addresses soft errors, which corrupt the task being executed by a processor but do not cause the entire memory of that processor to be lost, contrarily to fail-stop errors. We revisit classical mapping heuristics such as HEFT and MinMin and complement them with several checkpointing strategies. The objective is to derive an efficient trade-off between checkpointing every task (CkptAll), which is an overkill when failures are rare events, and checkpointing no task (CkptNone), which induces dramatic re-execution overhead even when only a few failures strike during execution. Contrarily to previous work, our approach applies to arbitrary workflows, not just special classes of dependence graphs such as M-SPGs (Minimal Series-Parallel Graphs). Extensive experiments report significant gain over both CkptAll and CkptNone, for a wide variety of workflows.

Scientific workflows are frequently modeled as Directed Acyclic Graphs (DAG) of tasks, which represent computational modules and their dependencies, in the form of data produced by a task and used by another one. This formulation allows the use of runtime systems which dynamically allocate tasks onto the resources of increasingly complex and heterogeneous computing platforms. However, for some workflows, such a dynamic schedule may run out of memory by exposing too much parallelism. This paper focuses on the problem of transforming such a DAG to prevent memory shortage, and concentrates on shared memory platforms. We first propose a simple model of DAG which is expressive enough to emulate complex memory behaviors. We then exhibit a polynomial-time algorithm that computes the maximum memory peak of a DAG, that is, the maximum memory needed by any parallel schedule. We consider the problem of reducing this maximum memory peak to make it smaller than a given bound by adding new fictitious edges, while trying to minimize the critical path of the graph. After proving this problem NP-complete, we provide an ILP solution as well as several heuristic strategies that are thoroughly compared by simulation on both synthetic and actual computation DAGs. We show that on most instances, we are able to decrease the maximum memory peak at the cost of a small increase in the critical path, thus with little impact on quality of the final parallel schedule.

This paper discusses scheduling strategies for the problem of maximizing the expected number of tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The execution times of tasks follow IID probability laws. The main questions are how many processors to enroll and whether and when to interrupt tasks that have been executing for some time. We provide complexity results and an asymptotically optimal strategy for the problem instance with discrete probability distributions and without deadline. We extend the latter strategy for the general case with continuous distributions and a deadline and we design an efficient heuristic which is shown to outperform standard approaches when running simulations for a variety of useful distribution laws.

We consider the problem of orchestrating the execution of workflow applications structured as Directed Acyclic Graphs (DAGs) on parallel computing platforms that are subject to fail-stop failures. The objective is to minimize expected overall execution time, or makespan. A solution to this problem consists of a schedule of the workflow tasks on the available processors and of a decision of which application data to checkpoint to stable storage, so as to mitigate the impact of processor failures. To address this challenge, we consider a restricted class of graphs, Minimal Series-Parallel Graphs (M-SPGS), which is relevant to many real-world workflow applications. For this class of graphs, we propose a recursive list-scheduling algorithm that exploits the M-SPG structure to assign sub-graphs to individual processors, and uses dynamic programming to decide how to checkpoint these sub-graphs. We assess the performance of our algorithm for production workflow configurations, comparing it to an approach in which all application data is checkpointed and an approach in which no application data is checkpointed. Results demonstrate that our algorithm outperforms both the former approach, because of lower checkpointing overhead, and the latter approach, because of better resilience to failures.

Scientific workloads are often described by Directed Acyclic task Graphs. Indeed, DAGs represent both a theoretical model and the structure employed by dynamic runtime schedulers to handle HPC applications. A natural problem is then to compute a makespan-minimizing schedule of a given graph. In this paper, we are motivated by task graphs arising from multifrontal factorizations of sparse matrices and therefore work under the following practical model. Tasks are malleable (i.e., a single task can be allotted a time-varying number of processors) and their speedup behaves perfectly up to a first threshold, then speedup increases linearly, but not perfectly, up to a second threshold where the speedup levels off and remains constant. After proving the NP-hardness of minimizing the makespan of DAGs under this model, we study several heuristics. We propose model-optimized variants for PROPSCHEDULING, widely used in linear algebra application scheduling, and FLOWFLEX. GREEDYFILLING is proposed, a novel heuristic designed for our speedup model, and we demonstrate that PROPSCHEDULING and GREEDYFILLING are 2-approximation algorithms. In the evaluation, employing synthetic data sets and task graphs arising from multifrontal factorization, the proposed optimized variants and GREEDYFILLING significantly outperform the traditional algorithms, whereby GREEDYFILLING demonstrates a particular strength for balanced graphs.

This paper revisits the failure1temporal independence hypothesis which is omnipresent in the analysis of resilience methods for HPC. We explain why a previous approach is incorrect, and we propose a new method to detect failure cascades, i.e., series of non-independent consecutive failures. We use this new method to assess whether public archive failure logs contain failure cascades. Then we design and compare several cascade-aware checkpointing algorithms to quantify the maximum gain that could be obtained, and we report extensive simulation results with archive and synthetic failure logs. Altogether, there are a few logs that contain cascades, but we show that the gain that can be achieved from this knowledge is not significant. The conclusion is that we can wrongly, but safely, assume failure independence!

We consider the problem of orchestrating the execution of workflow applications structured as Directed Acyclic Graphs (DAGs) on parallel computing platforms that are subject to fail-stop failures. The objective is to minimize expected overall execution time, or makespan. A solution to this problem consists of a schedule of the workflow tasks on the available processors and of a decision of which application data to checkpoint to stable storage, so as to mitigate the impact of processor failures. For general DAGs this problem is hopelessly intractable. In fact, given a solution, computing its expected makespan is still a difficult problem. To address this challenge, we consider a restricted class of graphs, Minimal Series-Parallel Graphs (M-SPGS). It turns out that many real-world workflow applications are naturally structured as M-SPGS. For this class of graphs, we propose a recursive list-scheduling algorithm that exploits the M-SPG structure to assign sub-graphs to individual processors, and uses dynamic programming to decide which tasks in these sub-gaphs should be checkpointed. Furthermore, it is possible to efficiently compute the expected makespan for the solution produced by this algorithm, using a first-order approximation of task weights and existing evaluation algorithms for 2-state probabilistic DAGs. We assess the performance of our algorithm for production workflow configurations, comparing it to (i) an approach in which all application data is checkpointed, which corresponds to the standard way in which most production workflows are executed today; and (ii) an approach in which no application data is checkpointed. Our results demonstrate that our algorithm strikes a good compromise between these two approaches, leading to lower checkpointing overhead than the former and to better resilience to failure than the latter.

The traditional single-level checkpointing method suffers from significant overhead on large-scale platforms. Hence, multilevel checkpointing protocols have been studied extensively in recent years. The multilevel checkpoint approach allows different levels of checkpoints to be set (each with different checkpoint overheads and recovery abilities), in order to further improve the fault tolerance performance of extreme-scale HPC applications. How to optimize the checkpoint intervals for each level, however, is an extremely difficult problem. In this paper, we construct an easy-to-use two-level checkpoint model. Checkpoint level 1 deals with errors with low checkpoint/recovery overheads such as transient memory errors, while checkpoint level 2 deals with hardware crashes such as node failures. Compared with previous optimization work, our new optimal checkpoint solution offers two improvements: (1) it is an online solution without requiring knowledge of the job length in advance, and (2) it shows that periodic patterns are optimal and determines the best pattern. We evaluate the proposed solution and compare it with the most up-to-date related approaches on an extreme-scale simulation testbed constructed based on a real HPC application execution. Simulation results show that our proposed solution outperforms other optimized solutions and can improve the performance significantly in some cases. Specifically, with the new solution the wall-clock time can be reduced by up to 25.3 percent over that of other state-of-the-art approaches. Finally, a brute-force comparison with all possible patterns shows that our solution is always within 1 percent of the best pattern in the experiments.

In this paper, we discuss several scheduling algorithms to execute independent tasks with voltage overscaling. Given a frequency to execute the tasks, operating at a voltage below threshold leads to significant energy savings but also induces timing errors. A verification mechanism must be enforced to detect these errors. Contrarily to fail-stop or silent errors, timing errors are deterministic (but unpredictable). For each task, the general strategy is to select a voltage for execution, to check the result, and to select a higher voltage for re-execution if a timing error has occurred, and so on until a correct result is obtained. Switching from one voltage to another incurs a given cost, so it might be efficient to try and execute several tasks at the current voltage before switching to another one. Determining the optimal solution turns out to be unexpectedly difficult. However, we provide the optimal algorithm for a single task, the optimal algorithm when there are only two voltages, and the optimal level algorithm for a set of independent tasks, where a level algorithm is defined as an algorithm that executes all remaining tasks when switching to a given voltage. Furthermore, we show that the optimal level algorithm is in fact globally optimal (among all possible algorithms) when voltage switching costs are linear. Finally, we report a comprehensive set of simulations to assess the potential gain of voltage overscaling algorithms.

The processing of queries expressed as trees of boolean operators applied to predicates on sensor data streams has several applications in mobile computing. Sensor data must be retrieved from the sensors, which incurs a cost, e.g., an energy expense that depletes the battery of a mobile query processing device. The objective is to determine the order in which predicates should be evaluated so as to shortcut part of the query evaluation and minimize the expected cost. This problem has been studied assuming that each data stream occurs at a single predicate. In this work we remove this assumption since it does not necessarily hold in practice. Our main results are an optimal algorithm for single-level trees and a proof of NP-completeness for DNF trees. For DNF trees, however, we show that there is an optimal predicate evaluation order that corresponds to a depth-first traversal. This result provides inspiration for a class of heuristics. We show that one of these heuristics largely outperforms other sensible heuristics, including a heuristic proposed in previous work.

SUMMARY In this paper, we present a unified model for several well‐known checkpoint/restart protocols. The proposed model is generic enough to encompass both extremes of the checkpoint/restart space, from coordinated approaches to a variety of uncoordinated checkpoint strategies (with message logging). We identify a set of crucial parameters, instantiate them, and compare the expected efficiency of the fault tolerant protocols, for a given application/platform pair. We then propose a detailed analysis of several scenarios, including some of the most powerful currently available high performance computing platforms, as well as anticipated Exascale designs. The results of this analytical comparison are corroborated by a comprehensive set of simulations. Altogether, they outline comparative behaviors of checkpoint strategies at very large scale, thereby providing insight that is hardly accessible to direct experimentation. Copyright © 2013 John Wiley & Sons, Ltd.

This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents a large IO file. A task can only be executed if all input and output files fit into memory, and a file can only be removed from memory after it has been consumed. Such trees arise, for instance, in the multifrontal method of sparse matrix factorization. The maximum amount of memory needed depends on the execution order of the tasks. With one processor the objective of the tree traversal is to minimize the required memory. This problem was well studied and optimal polynomial algorithms were proposed. Here, we extend the problem by considering multiple processors, which is of obvious interest in the application area of matrix factorization. With the multiple processors comes the additional objective to minimize the time needed to traverse the tree, i.e., to minimize the makespan. Not surprisingly, this problem proves to be much harder than the sequential one. We study the computational complexity of this problem and provide an inapproximability result even for unit weight trees. Several heuristics are proposed, each with a different optimization focus, and they are analyzed in an extensive experimental evaluation using realistic trees.

Platforms that comprise volatile processors, such as desktop grids, have been traditionally used for executing independent-task applications. In this work we study the scheduling of tightly-coupled iterative master-worker applications onto volatile processors. The main challenge is that workers must be simultaneously available for the application to make progress. We consider two additional complications: one should take into account that workers can become temporarily reclaimed and, for data-intensive applications, one should account for the limited bandwidth between the master and the workers. In this context, our first contribution is a theoretical study of the scheduling problem in its off-line version, i.e., when processor availability is known in advance. Even in this case the problem is NP-hard. Our second contribution is an analytical approximation of the expectation of the time needed by a set of workers to complete a set of tasks and of the probability of success of this computation. This approximation relies on a Markovian assumption for the temporal availability of processors. Our third contribution is a set of heuristics, some of which use the above approximation to favor reliable processors in a sensible manner. We evaluate these heuristics in simulation. We identify some heuristics that significantly outperform their competitors and derive heuristic design guidelines.

In this paper, we revisit traditional check pointing and rollback recovery strategies, with a focus on silent data corruption errors. Contrarily to fail-stop failures, such latent errors cannot be detected immediately, and a mechanism to detect them must be provided. We consider two models: (i) errors are detected after some delays following a probability distribution (typically, an Exponential distribution), (ii) errors are detected through some verification mechanism. In both cases, we compute the optimal period in order to minimize the waste, i.e., the fraction of time where nodes do not perform useful computations. In practice, only a fixed number of checkpoints can be kept in memory, and the first model may lead to an irrecoverable failure. In this case, we compute the minimum period required for an acceptable risk. For the second model, there is no risk of irrecoverable failure, owing to the verification mechanism, but the corresponding overhead is included in the waste. Finally, both models are instantiated using realistic scenarios and application/architecture parameters.

This paper deals with the impact of fault prediction techniques on check pointing strategies. We consider fault-prediction systems that do not provide exact prediction dates, but instead time intervals during which faults are predicted to strike. These intervals dramatically complicate the analysis of the check pointing strategies. We propose a new approach based upon two periodic modes, a regular mode outside prediction windows, and a proactive mode inside prediction windows, whenever the size of these windows is large enough. We are able to compute the best period for any size of the prediction windows, thereby deriving the scheduling strategy that minimizes platform waste. In addition, the results of the analytical study are nicely corroborated by a comprehensive set of simulations, which demonstrate the validity of the model and the accuracy of the approach.

In this paper, we aim at optimizing fault-tolerance techniques based on a checkpointing/restart mechanism, in the context of cloud computing. Our contribution is three-fold. (1) We derive a fresh formula to compute the optimal number of checkpoints for cloud jobs with varied distributions of failure events. Our analysis is not only generic with no assumption on failure probability distribution, but also attractively simple to apply in practice. (2) We design an adaptive algorithm to optimize the impact of checkpointing regarding various costs like checkpointing/restart overhead. (3) We evaluate our optimized solution in a real cluster environment with hundreds of virtual machines and Berkeley Lab Checkpoint/Restart tool. Task failure events are emulated via a production trace produced on a large-scale Google data center. Experiments confirm that our solution is fairly suitable for Google systems. Our optimized formula outperforms Young's formula by 3-10 percent, reducing wall-clock lengths by 50-100 seconds per job on average.

We propose algorithms for allocating multiple resources to competing services running in virtual machines on heterogeneous distributed platforms. We develop a theoretical problem formulation and compare these algorithms via simulation experiments based in part on workload data supplied by Google. Our main finding is that vector packing approaches proposed in the homogeneous case can be extended to provide high-quality solutions in the heterogeneous case, and combined to provide a single efficient algorithm. We also consider the case when there may be bounded errors in estimates of performance-related resource needs. We provide a heuristic for compensating for such errors that performs well in simulation, as well as a proof of the worst-case competitive ratio for the single-resource, single-node case when there is no bound on the error.

We propose a novel job scheduling approach for homogeneous cluster computing platforms. Its key feature is the use of virtual machine technology to share fractional node resources in a precise and controlled manner. Other VM-based scheduling approaches have focused primarily on technical issues or extensions to existing batch scheduling systems, while we take a more aggressive approach and seek to find heuristics that maximize an objective metric correlated with job performance. We derive absolute performance bounds and develop algorithms for the online nonclairvoyant version of our scheduling problem. We further evaluate these algorithms in simulation against both synthetic and real-world HPC workloads and compare our algorithms to standard batch scheduling approaches. We find that our approach improves over batch scheduling by orders of magnitude in terms of job stretch, while leading to comparable or better resource utilization. Our results demonstrate that virtualization technology coupled with lightweight online scheduling strategies can afford dramatic improvements in performance for executing HPC workloads.

In this paper we study the execution of iterative applications on volatile processors such as those found on desktop grids. We develop master-worker scheduling schemes that attempt to achieve good trade-offs between worker speed and worker availability. A key feature of our approach is that we consider a communication model where the bandwidth capacity of the master for sending application data to workers is limited. This limitation makes the scheduling problem more difficult both in a theoretical sense and in a practical sense. Furthermore, we consider that a processor can be in one of three states: available, down, or temporarily preempted by its owner. This preempted state also complicates the scheduling problem. In practical settings, e.g., desktop grids, master bandwidth is limited and processors are temporarily reclaimed. Consequently, addressing the aforementioned difficulties is necessary for successfully deploying master-worker applications on volatile platforms. Our first contribution is to determine the complexity of the scheduling problem in its off-line version, i.e., when processor availability behaviors are known in advance. Even with this knowledge, the problem is NP-hard, and cannot be approximated within a factor $8/7$. Our second contribution is a closed-form formula for the expectation of the time needed by a worker to complete a set of tasks. This formula relies on a Markovian assumption for the temporal availability of processors, and is at the heart of some heuristics that aim at favoring "reliable'' processors in a sensible manner. Our third contribution is a set of heuristics, which we evaluate in simulation. Our results provide guidance to selecting the best strategy as a function of processor state availability versus average task duration.

This work provides an analysis of checkpointing strategies for minimizing expected job execution times in an environment that is subject to processor failures. In the case of both sequential and parallel jobs, we give the optimal solution for exponentially distributed failure inter-arrival times, which, to the best of our knowledge, is the first rigorous proof that periodic checkpointing is optimal. For non-exponentially distributed failures, we develop a dynamic programming algorithm to maximize the amount of work completed before the next failure, which provides a good heuristic for minimizing the expected execution time. Our work considers various models of job parallelism and of parallel checkpointing overhead. We first perform extensive simulation experiments assuming that failures follow Exponential or Weibull distributions, the latter being more representative of real-world systems. The obtained results not only corroborate our theoretical findings, but also show that our dynamic programming algorithm significantly outperforms previously proposed solutions in the case of Weibull failures. We then discuss results from simulation experiments that use failure logs from production clusters. These results confirm that our dynamic programming algorithm significantly outperforms existing solutions for real-world clusters.

Abstract We consider the problem of scheduling an application composed of independent tasks on a fully heterogeneous master–worker platform with communication costs. We introduce a bi‐criteria approach aiming at maximizing the throughput of the application while minimizing the energy consumed by participating resources. Assuming arbitrary super‐linear power consumption laws, we investigate different models, with energy overheads and memory constraints. Building upon closed‐form expressions for the uni‐processor case, we derive asymptotically optimal solutions for all models. Copyright © 2010 John Wiley & Sons, Ltd.

We propose a novel job scheduling approach for homogeneous cluster computing platforms. Its key feature is the use of virtual machine technology for sharing resources in a precise and controlled manner. We justify our approach and propose several job scheduling algorithms. We present results obtained in simulations for synthetic and real-world High Performance Computing (HPC) workloads, in which we compare our proposed algorithms with standard batch scheduling algorithms. We find that our approach widely outperforms batch scheduling. We also identify a few promising algorithms that perform well across most experimental scenarios. Our results demonstrate that virtualization technology coupled with lightweight scheduling strategies affords dramatic improvements in performance for HPC workloads.

Scheduling problems are already difficult on traditional parallel machines, and they become extremely challenging on heterogeneous clusters. In this paper, we deal with the problem of scheduling multiple applications, made of collections of independent and identical tasks, on a heterogeneous master-worker platform. The applications are submitted online, which means that there is no a priori (static) knowledge of the workload distribution at the beginning of the execution. The objective is to minimize the maximum stretch, i.e., the maximum ratio between the actual time an application has spent in the system and the time this application would have spent if executed alone. On the theoretical side, we design an optimal algorithm for the offline version of the problem (when all release dates and application characteristics are known beforehand). We also introduce a heuristic for the general case of online applications. On the practical side, we have conducted extensive simulations and MPI experiments, showing that we are able to deal with very large problem instances in a few seconds. Also, the solution that we compute totally outperforms classical heuristics from the literature, thereby fully assessing the usefulness of our approach.

We propose a novel approach for sharing cluster resources among competing jobs. The key advantage of our approach over current solutions is that it increases cluster utilization while optimizing a user-centric metric that captures both notions of performance and fairness. We motivate and formalize the corresponding resource allocation problem, determine its complexity, and propose several algorithms to solve it in the case of a static workload that consists of sequential jobs. Via extensive simulation experiments we identify an algorithm that runs quickly, that is always on par with or better than its competitors, and that produces resource allocations that are close to optimal. We find that the extension of our approach to parallel jobs leads to similarly good results. Finally, we explain how to extend our work to dynamic workloads.

In this paper, we deal with the large-scale divisible load problem studied in. We show how to reduce this problem to a classical preemptive scheduling problem on a single machine, thereby establishing new complexity results, and providing new approximation algorithms and heuristics that subsume those presented in. We also give some hints on how to extend the results to a more realistic framework where communication costs are taken into account.

One has a large workload that is ldquodivisiblerdquo-its constituent work's granularity can be adjusted arbitrarily;-and one has access to p remote computers that can assist in computing the workload. The problem is that the remote computers are subject to interruptions of known likelihood that kill all work in progress. One wishes to orchestrate sharing the workload with the remote computers in a way that maximizes the expected amount of work completed. Strategies for achieving this goal, by balancing the desire to checkpoint often, in order to decrease the amount of vulnerable work at any point, vs. the desire to avoid the context-switching required to checkpoint, are studied. Strategies are devised that provably maximize the expected amount of work when there is only one remote computer (the case p = 1). Results suggest the intractability of such maximization for higher values of p, which motivates the development of heuristic approaches. Heuristics are developed that replicate works on several remote computers, in the hope of thereby decreasing the impact of work-killing interruptions. The quality of these heuristics is assessed through exhaustive simulations.

In this paper, we focus on scheduling jobs on computing grids. In our model, a grid job is made of a large collection of input data sets, which must all be processed by the same task graph or workflow, thus resulting in a collection of task graphs problem. We are looking for a competitive scheduling algorithm not requiring complex control. We thus only consider single-allocation strategies. In addition to a mixed linear programming approach to find an optimal allocation, we present different heuristic schemes. Then, using simulations, we compare the performance of our different heuristics to the performance of a classical scheduling policy in Grids, HEFT. The results show that some of our static-scheduling policies take advantage of their platform and application knowledge and outperform HEFT, especially under communication-intensive scenarios. In particular, one of our heuristics, DELEGATE, almost always achieves the best performance while having lower running times than HEFT.

In this paper, we focus on scheduling jobs on computing Grids. In our model, a Grid job is made of a large collection of input data sets, which must all be processed by the same task graph or workflow, thus resulting in a series of workflow problem. We are looking for an efficient solution with regard to throughput and latency, while avoiding solutions requiring complex control. We thus only consider single-allocation strategies. We present an algorithm based on mixed linear programming to find an optimal allocation, and this for different routing policies depending on how much latitude we have on communications. Then, using simulations, we compare our allocations to reference heuristics. The results show that our algorithm almost always finds an allocation with good throughput and low latency, and that it outperforms the reference heuristics, especially under communication-intensive scenarios.

The resolution of combinatorial assortments of protein sequences into domains is a prerequisite for protein sequence interpretation. However the recognition and clustering of homologous domains from sequence databases typically scales quadratically with respect to their size which grows exponentially, making it essential to parallelize these complex bioinformatics applications. Here we demonstrate the parallelization of MKDOM2, the sequential program that has been instrumental in the construction of the PRODOM database of protein domain families. This was challenging because of (1) dependencies between program iterations, (2) their extremely heterogeneous run times and (3) communication bottlenecks that could arise because of the large size of the data. A large scale test of the new program, MPI_MKDOM2, demonstrated its robustness against heterogeneous run times, preparing the grounds for future releases of PRODOM that would otherwise be out of reach with MKDOM2 by several orders of magnitude.

Scheduling problems are already difficult on traditional parallel machines. They become extremely challenging on heterogeneous clusters, even when embarrassingly parallel applications are considered. In this paper we deal with the problem of scheduling multiple applications, made of collections of independent and identical tasks, on a heterogeneous master-worker platform. The applications are submitted online, which means that there is no a priori (static) knowledge of the workload distribution at the beginning of the execution. The objective is to minimize the maximum stretch, i.e. the maximum ratio between the actual time an application has spent in the system and the time this application would have spent if executed alone. On the theoretical side, we design an optimal algorithm for the offline version of the problem (when all release dates and application characteristics are known beforehand). We also introduce several heuristics for the general case of online applications. On the practical side, we have conducted extensive simulations and MPI experiments, showing that we are able to deal with very large problem instances in a few seconds. Also, the solution that we compute totally outperforms classical heuristics from the literature, thereby fully assessing the usefulness of our approach.

This paper is focused on designing efficient parallel matrix-product algorithms for heterogeneous master-worker platforms. While matrix-product is well-understood for homogeneous 2D-arrays of processors (e.g., Cannon algorithm and ScaLAPACK outer product algorithm), there are three key hypotheses that render our work original and innovative:

Min, Veeravalli, and Barlas have recently proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments [18, 19]. We show on a very simple example that their approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal scheduling for any instance, once the number of installments per load is given. Then, we formally prove that any optimal schedule has an infinite number of installments under a linear cost model as the one assumed in [18, 19]. Such a cost model cannot be used to design practical multi-installment strategies. Finally, through extensive simulations we confirmed that the best solution is always produced by the linear programming approach.

This paper is aimed at designing efficient parallel matrix-product algorithms for homogeneous master-worker platforms. While matrix-product is well-understood for homogeneous 2D-arrays of processors (e.g., Cannon algorithm and ScaLAPACK outer product algorithm), there are two key hypotheses that render our work original and innovative: 1) centralized data: we assume that all matrix files originate from, and must be returned to, the master. The master distributes both data and computations to the workers (while in ScaLAPACK, input and output matrices are initially distributed among participating resources). Typically, our approach is useful in the context of speeding up MATLAB or SCILAB clients running on a server (which acts as the master and initial repository of files). 2) Limited memory: because we investigate the parallelization of large problems, we cannot assume that full matrix panels can be stored in the worker memories and re-used for subsequent updates (as in ScaLAPACK). The amount of memory available in each worker is expressed as a given number of buffers, where a buffer can store a square block of matrix elements. These square blocks are chosen so as to harness the power of level 3 BIAS routines; they are of size 80 or 100 on most platforms. We have devised efficient algorithms for resource selection (deciding which workers to enroll) and communication ordering (both for input and result messages), and we report a set of MPI experiments conducted on a platform at the University of Tennessee.

In this paper, we study the problem of scheduling file transfers through a switch. This problem is at the heart of a model often used for large grid computations, where the switch represents the core of the network interconnecting the various clusters that compose the grid. We establish several complexity results, and we introduce and analyze various algorithms, from both a theoretical and a practical perspective

In this work we are interested in the problem of scheduling and redistributing data on master-slave platforms. We consider the case were the workers possess initial loads, some of which having to be redistributed in order to balance their completion times. We assume that the data consists of independent and identical tasks. As the general case is NP-complete in the strong sense, we propose three heuristics. Simulations consolidate the theoretical results

We present a unified mathematical framework for analyzing the tradeoffs between parallelism and storage allocation within a parallelizing compiler. Using this framework, we show how to find a good storage mapping for a given schedule, a good schedule for a given storage mapping, and a good storage mapping that is valid for all legal (one-dimensional affine) schedules. We consider storage mappings that collapse one dimension of a multidimensional array, and programs that are in a single assignment form and accept a one-dimensional affine schedule. Our method combines affine scheduling techniques with occupancy vector analysis and incorporates general affine dependences across statements and loop nests. We formulate the constraints imposed by the data dependences and storage mappings as a set of linear inequalities, and apply numerical programming techniques to solve for the shortest occupancy vector. We consider our method to be a first step towards automating a procedure that finds the optimal tradeoff between parallelism and storage space.

In this paper we study how distributed scheduling systems can be designed most effectively; we focus on the problem of selecting an optimal arrangement of schedulers, or a deployment, for hierarchically organized systems. We show that the optimal deployment is a complete spanning d-ary tree; this result conforms with results from the scheduling literature. More importantly, we present an approach for determining the optimal degree d for the tree. We test our approach using DIET, a network-enabled server system that uses hierarchical schedulers. Finally, we demonstrate that our approach selects deployments that are near-optimal in practice

In this paper, we assess the impact of heterogeneity for scheduling independent tasks on master-slave platforms. We assume a realistic one-port model where the master can communicate with a single slave at any time-step. We target online scheduling problems, and we focus on simpler instances where all tasks have the same size. While such problems can be solved in polynomial time on homogeneous platforms, we show that there does not exist any optimal deterministic algorithm for heterogeneous platforms. Whether the source of heterogeneity comes from computation speeds, or from communication bandwidths, or from both, we establish lower bounds on the competitive ratio of any deterministic algorithm. We provide such bounds for the most important objective functions: the minimization of the makespan (or total execution time), the minimization of the maximum response time (difference between completion time and release time), and the minimization of the sum of all response times. Altogether, we obtain nine theorems which nicely assess the impact of heterogeneity on online scheduling. These theoretical contributions are complemented on the practical side by the implementation of several heuristics on a small but fully heterogeneous MPI platform. Our (preliminary) results show the superiority of those heuristics which fully take into account the relative capacity of the communication links.

In this paper, we deal with the problem of scheduling independent tasks on heterogeneous master-slave platforms. We target both off-line and on-line problems, with several objective functions (makespan, maximum response time, total completion time). On the theoretical side, our results are two-fold: (i) For offline scheduling, we prove several optimality results for problems with release dates; (ii) For on-line scheduling, we establish lower bounds on the competitive ratio of any deterministic algorithm. On the practical side, we have implemented several heuristics, some classical and some new ones derived in this paper, on a small but fully heterogeneous MPI platform. Our results show the superiority of those heuristics which fully take into account the relative capacity of the communication links.

In this paper, we consider the problem of scheduling distributed biological sequence comparison applications. This problem lies in the divisible load framework with negligible communication costs. Thus far, very few results have been proposed in this model. We discuss and select relevant metrics for this framework: namely max-stretch and sumstretch. We explain the relationship between our model and the preemptive uni-processor case, and we show how to extend algorithms that have been proposed in the literature for the uni-processor model to the divisible multi-processor problem domain. We recall known results on closely related problems, derive new lower bounds on the competitive ratio of any on-line algorithm, present new competitiveness results for existing algorithms, and develop several new online heuristics. Then, we extensively study the performance of these algorithms and heuristics in realistic scenarios. Our study shows that all previously proposed guaranteed heuristics for max-stretch for the uni-processor model prove to be particularly inefficient in practice. In contrast, we show our on-line algorithms based on linear programming to be nearoptimal solutions for max-stretch. Our study also clearly suggests heuristics that are efficient for both metrics, although a combined optimization is in theory not possible in the general case.

We consider the mapping of iterative algorithms onto heterogeneous clusters. The application data is partitioned over the processors, which are arranged along a virtual ring. At each iteration, independent calculations are carried out in parallel, and some communications take place between consecutive processors in the ring. The aim is to determine how to slice the application data into chunks, and to assign these chunks to the processors, so that the total execution time is minimized. One major difficulty is to embed a processor ring into a network that typically is not fully connected, so that some communication links have to be shared by several processor pairs. We establish a complexity result that assesses the difficulty of this problem, and we design a practical heuristic that provides efficient mapping, routing, link- sharing, and data distribution schemes.

Abstract Feautrier's scheduling algorithm is the most powerful existing algorithm for parallelism detection and extraction, but it has always been known to be suboptimal. However, the question as to whether it may miss some parallelism because of its design has not been answered. We show that this is not the case. Therefore, for an algorithm to find more parallelism than this algorithm, one needs to remove some of the hypotheses underlying its framework. Copyright © 2003 John Wiley & Sons, Ltd.

We present two new results of importance in code generation for and synthesis of synchronously scheduled parallel processor arrays and multicluster VLIWs. The first is a new practical method for constructing a linear schedule for the iterations of a loop nest that schedules precisely one iteration per cycle on each of a prescribed set of processors. While this problem goes back to the era in which systolic computation was in vogue, it has defied practical solution until now. We provide a closed form solution that enables the enumeration of all such schedules. The second result is a new technique that reduces the cost of code or hardware whose function is to control the flow of data and predicate operations, and to generate memory addresses. The key idea is that by using the mathematical structure of any of the conflict-free schedules we construct, a very shallow recurrence can be developed to inexpensively update these quantities.

We present a unified mathematical framework for analyzing the tradeoffs between parallelism and storage allocation within a parallelizing compiler. Using this framework, we show how to find a good storage mapping for a given schedule, a good schedule for a given storage mapping, and a good storage mapping that is valid for all legal schedules. We consider storage mappings that collapse one dimension of a multi-dimensional array, and programs that are in a single assignment form with a one-dimensional schedule. Our technique combines affine scheduling techniques with occupancy vector analysis and incorporates general affine dependences across statements and loop nests. We formulate the constraints imposed by the data dependences and storage mappings as a set of linear inequalities, and apply numerical programming techniques to efficiently solve for the shortest occupancy vector. We consider our method to be a first step towards automating a procedure that finds the optimal tradeoff between parallelism and storage space.

We present a new pointer and escape analysis. Instead of analyzing the whole program, the algorithm incrementally analyzes only those parts of the program that may deliver useful results. An analysis policy monitors the analysis results to direct the incremental investment of analysis resources to those parts of the program that offer the highest expected optimization return.

We describe a new, practical, constructive method for solving the well-known conflict-free scheduling problem for the locally sequential, globally parallel (LSGP) case of processor array synthesis. First, we provide a closed form solution that enables the enumeration of all conflict-free schedules. Then, we discuss the reduction of the cost of hardware whose function is to control the flow of data, enable or disable functional units, and generate memory addresses. We present a new technique for controlling the complexity of these housekeeping functions in a processor array. Both of these techniques have been incorporated into a software system for the automatic synthesis of hardware accelerators developed by HP Labs.

This paper is devoted to a low-complexity algorithm for retiming circuits without cycles, i.e., those whose network graph is a direct acyclic graph (DAG). On one hand, DAGs have a great practical importance, as shown by the on-line arithmetic circuits used as a target application in this paper. On the other hand, retiming is a costly design optimization technique, in particular when applied to large circuits. Hence the need to design a specialized retiming algorithm to handle DAGs more efficiently than general-purpose retiming algorithms. Our algorithm dramatically improves on current solutions in the literature. We gain an order of magnitude in the worst case complexity, and we show convincing experimental results at the end of this paper.

In this paper we build upon results of D.A. Padua and M.J. Wolfe (1986), who introduce two graph transformations to eliminate anti and output dependences. We first give a unified framework for such transformations. Then, given a loop nest, we aim at determining which statements should be transformed so as to break artificial cycles involving anti or output dependences. The problem of finding the mininum number of statements to be transformed is shown to be NP-complete in the strong sense, and we propose two efficient heuristics.

This paper is devoted to the construction of multi-dimensional schedules for a system of uniform recurrence equations. We show that this problem is dual to the problem of computability of a system of uniform recurrence equations. We propose a new study of the decomposition algorithm first proposed by Karp, Miller and Winograd: we base our implementation on linear programming resolutions whose duals give exactly the desired multi-dimensional schedules. Furthermore, we prove that the schedules built this way are optimal up to a constant factor.